Department of Mathematics
United States of America
Dr. Raines received his doctorate in mathematics from Oxford University where he was a member of St. Edmund's Hall. He travels extensively to work with collaborators in the UK, Italy, and Croatia. He was born and raised in Texas. He is married with two children, and loves to cook and play games of all sorts. Dr. Raines research is in the topology of pathological spaces that arise in dynamical systems. He is also interested in applications of topology to non-deterministic dynamical systems that arise in mathematical economics.
topology of pathological spaces
"Basins of measures on inverse limit spaces for the induced homeomorphism," joint with J. Kennedy and D. Stockman, Ergodic Theory and Dynamical Systems 30 (2010) 1119-1130.
"Fixed points imply chaos for a class of differential inclusions that arise in economic models," joint with D. Stockman, Transactions of the AMS (2011) to appear 1-18.
"A compact metric space that is universal for orbit spectra of homeomorphisms," joint with C. Good, S. Greenwood and C. Sherman, Advances in Mathematics (2011) to appear 1-14.